**Ans . **

Rs. 5880

**Explanation :**Face value of the bill = Rs. 6000.

Date on which the bill was drawn = July 14 at 5 months. Nominally due date =December 14.,Legally due date = December 17.

Date on which the bill was discounted = October 5. Unexpired time : Oct. Nov. Dec.

26 + 30 + 17 = 73 days =1/ 5Years

B.D. = S.I. on Rs. 6000 for 1/5 year= Rs. (6000 x 10 x1/5 x1/100)= Rs. 120.

T.D. = Rs.[(6000 x 10 x1/5)/(100+(10*1/5))]=Rs.(12000/102)=Rs. 117.64.

B.G. = (B.D.) - (T.D.) = Rs. (120 - 117.64) = Rs. 2.36. Money received by the holder of the bill = Rs. (6000 - 120)= Rs. 5880..

**Ans . **

Rs. 129

**Explanation :**B.G. = S.I. on T.D.

= Rs.(120 x 15 x 1/2 x 1/100)= Rs. 9.

(B.D.) - (T.D.) = Rs. 9.

B.D. = Rs. (120 + 9) = Rs. 129.

**Ans . **

4 months

**Explanation :**S.I. on Rs. 1800 = T.D. on Rs. 1872.

P.W. of Rs. 1872 is Rs. 1800.

Rs. 72 is S.I. on Rs. 1800 at 12%.

Time =[(100 x 72)/ (12x1800)]year=1/3year = 4 months.

**Ans . **

13 7/11%

**Explanation :**Sum =[( B.D.*T.D.)/(B.D.-T.D.)] = Rs.[(120x110)/(120-110)]= Rs. 1320. Since B.D. is S.I. on sum due, so S.I. on Rs. 1320 for 8 months is Rs. 120. Rate =[(100 x120)/( 1320 x 2/3)%= 13 7/11%.

**Ans . **

Rs. 121

**Explanation :**T.D. =\(\sqrt{(P.W.*B.G)}\)

B.G. =\(\frac{(T.D.)^2}{P.W}\) = Rs.[(110x110)/ 1100]= Rs. 11.

B.D.= (T.D. + B.G.) = Rs. (110 + 11) = Rs. 121..

**Ans . **

Rs 15

**Explanation :**Sum = [(B.D.xT.D.)/ (B.D.-T.D.)]= [(B.D.xT.D.)/B.G.]

T.D./B.G. = Sum/ B.D.=1650/165=10/1

Thus, if B.G. is Re 1, T.D. = Rs. 10.

If B.D.is Rs. ll, T.D.=Rs. 10.

If B.D. is Rs. 165, T.D. = Rs. [(10/11)xl65]=Rs.150

And, B.G. = Rs. (165 - 150) = Rs 15.

**Ans . **

13 1/3%

**Explanation :**Let amount of the bill = Rs.100

Money deducted =Rs.10

Money received by the holder of the bill = Rs.100-10 = Rs.90

SI on Rs.90 for 10 months = Rs.10

Rate =[(100*10)/(90*10/12)%=13 1/3%